This article is a discussion of a dominant (and mostly taken-for-granted) discourse of multicultural education (the phrase ‘intercultural education’ is sometimes used). My aim is, simply, to highlight two issues which, I think, are insufficiently dealt with in relation to multicultural education: the observation that differences can be irreconcilable and the idea of change. In the first part of this article, I try to sketch this discourse by giving some examples in which some characteristic markers of this discourse are illustrated (such as the idea of initiation in a variety of perspectives, of inclusion of a diversity of viewpoints, hearing multiple voices, of enrichment of our own way of looking at the world, etc.). In the second part of this article, I will rehearse some familiar concepts regarding what it means to be initiated into socio-historical and cultural practices, drawing mainly on Cavell. The point here is to bring out a sense of a human being’s embeddedness in a form of life that at the same time cuts very deep (i.e. affectively, even physically, anchored) and is incomplete (i.e. there is an irreducible, though unidentifiable lack), for the purpose of addressing the two issues mentioned (irreconcilable differences and change). Here the theme of voice (and what is involved in owning a voice) will be briefly developed, again by drawing on Cavell. In the final part of this article, will try to draw some implications for multicultural education.